Reflection Analysis of Spherical FDTD Absorbing Boundary Conditions

A system of equations is derived for the purpose of predicting numerical performance of absorbing boundary conditions for the finite-difference time-domain method in spherical coordinates. Multi-layer reflection analysis, coupled with spherical wave functions, are used to construct this system of equations. Subsequent analysis detail the strong performance dependence on ABC's radial distance and rotational mode orders. Obtained results can serve to design and/or develop efficient spherical FDTD absorbing boundary conditions.